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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.98.

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Elliptic curve cryptosystems
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by Neal Koblitz PDF
Math. Comp. 48 (1987), 203-209 Request permission


We discuss analogs based on elliptic curves over finite fields of public key cryptosystems which use the multiplicative group of a finite field. These elliptic curve cryptosystems may be more secure, because the analog of the discrete logarithm problem on elliptic curves is likely to be harder than the classical discrete logarithm problem, especially over ${\text {GF}}({2^n})$. We discuss the question of primitive points on an elliptic curve modulo p, and give a theorem on nonsmoothness of the order of the cyclic subgroup generated by a global point.
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Additional Information
  • © Copyright 1987 American Mathematical Society
  • Journal: Math. Comp. 48 (1987), 203-209
  • MSC: Primary 94A60; Secondary 11T71, 11Y16, 68P25
  • DOI:
  • MathSciNet review: 866109